February 2010
Volume 51, Issue 2
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Clinical and Epidemiologic Research  |   February 2010
Parameters Associated with the Different Astigmatism Axis Orientations
Author Affiliations & Notes
  • Yossi Mandel
    From the Israel Defense Force Medical Corps Headquarters, Ramat-Gan, Israel;
    the Hebrew University, Center for Bioengineering in the Service of Humanity and Society, Jerusalem, Israel;
  • Richard A. Stone
    the Department of Ophthalmology, University of Pennsylvania, Scheie Eye Institute, Philadelphia, Pennsylvania; and
  • David Zadok
    the Department of Ophthalmology, Assaf Harofeh Medical Center, Tel Aviv University, Zrifin, Israel.
  • Corresponding author: Yossi Mandel, The Selim and Rachel Benin School of Computer Science and Engineering, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel; yossimandel@bezeqint.net
Investigative Ophthalmology & Visual Science February 2010, Vol.51, 723-730. doi:10.1167/iovs.09-4356
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      Yossi Mandel, Richard A. Stone, David Zadok; Parameters Associated with the Different Astigmatism Axis Orientations. Invest. Ophthalmol. Vis. Sci. 2010;51(2):723-730. doi: 10.1167/iovs.09-4356.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: To evaluate parameters associated with astigmatism axis orientation.

Methods.: A retrospective population-based study was conducted on 67,899 (53% males) Israeli Defense Force conscripts aged 16 to 22 years with ≥0.25 D of astigmatism, using prerecruitment examination and demographic data that included a validated general intelligence score. Refractive errors were classified by the cylinder axis with the least deviation from emmetropia (LDE), a scheme intended to avoid confounding spherical classification by cylinder power. Perinatal photoperiod was determined from birth date and astronomical tables.

Results.: With-the-rule (WTR) axis was associated with higher LDE (P < 0.001), higher cylinder power (P < 0.001), Eastern or Western compared with Israeli origin (P < 0.001), higher body mass index (P < 0.001), lower intelligence scores (P < 0.001), and longer perinatal photoperiod (P < 0.001), using univariate analysis. Multivariate logistic regression confirmed the independent association of these parameters and identified being of the female sex as another WTR axis association. Subjects' cylinder axis also was associated with their siblings' cylinder axis (odds ratio [OR] = 1.58; 95% confidence interval [CI] = 1.31–1.90), using siblings' refractive data for the 3852 available subjects in the regression model. However, the associations of these parameters with WTR, against-the-rule, or oblique astigmatism were neither parallel as a whole nor parallel between any two sets of axis orientations. Further, the directions of the associations of these parameters with astigmatism axis and power did not consistently conform to their previously reported associations for spherical ametropias.

Conclusions.: The results suggest both that distinctive mechanisms may account for the different astigmatism axis orientations and that mechanisms influencing astigmatism development are likely to vary from those governing the spherical component of refraction.

Despite its clinical importance, little is understood about the risk factors and developmental processes leading to astigmatism. Refractive development in young animals is largely governed by visual input. 1 For example, the eyes of young chicks and many mammals, including monkeys, alter their growth to compensate for image defocus induced by concave (minus) or convex (plus) spectacle lenses, to maintain the photoreceptor position conjugate with the focal position of distant images. Although considerably less animal research has addressed the development of astigmatism, rearing animals with toric spectacle lenses does alter overall refractive development, but the responses do not compensate as precisely for astigmatic defocus as for spherical defocus in either chicks or monkeys. 24,5 In addition, infant monkeys show little spontaneous astigmatism compared with children. 5 It is unknown whether any of these animal results are pertinent to mechanisms underlying human astigmatism. Perhaps the lessening of astigmatism in young monkeys reared under visual conditions inducing ametropias 3 relates to the lessening of astigmatism occurring in human infants. 6,7 Regardless, these available data suggest that mechanisms underlying astigmatism may differ from those responsible for spherical ametropia. 
Astigmatism is commonly encountered clinically, with prevalence rates up to 30% or higher depending on the age or ethnic groups surveyed. 6,8 Human infants exhibit both high prevalence and high degrees of astigmatism, largely corneal in origin. 7,9 Based on available data, astigmatism lessens in prevalence and amplitude over the first few years of childhood, with an axis shift from against-the-rule (ATR) to with-the-rule (WTR). 7 Besides ethnic differences, some but not all studies find higher rates of astigmatism among subjects with ametropia in either the myopic or hyperopic direction, particularly for higher magnitude spherical refractive errors. 10,11 The limited evaluations of a genetic basis for astigmatism are conflicting 7 and do not clearly distinguish the relative roles of hereditary and environment. 
Epidemiologic studies examining ametropia typically address long-hypothesized clinically identifiable parameters—for example, including family history, near work, education, intelligence, socioeconomic status, or diet. 12 Most of these reports have isolated the spherical component of refractive error, not astigmatism. Recent studies also have suggested that childhood refractive development might be modulated by perinatal or even prenatal influences, including lighting, season of birth, diet, or chemical exposures (Fotedar R, et al. IOVS 2008;49:ARVO E-Abstract 3142). 1317 To our knowledge, none of these latter novel parameters have been studied for their potential associations with astigmatism. 
Accordingly, we assessed the associations of astigmatic refractive errors in a large population of military conscripts that was recently evaluated for risk factors for spherical ametropia. 15 By restricting the evaluation to subjects with astigmatism, we hoped to isolate parameters associated with the amplitude and axis of astigmatic refractive errors. 
Methods
Subjects
Military service in Israel is compulsory except for specific minority populations. Candidates for inclusion in our study comprised 328,905 (186,335 male and 142,570 female) subjects between 16 and 22 years of age who were examined in prerecruitment offices in the years 2000 through 2004 and who had refractive evaluation. All data were obtained from the database of the Israel Defense Forces Induction Center, without any details of personal identity. Origin was defined according to the father's country of birth or, for subjects whose father was born in Israel, by the grandfather's country of birth. Origin was categorized as Israeli, Western (countries of Europe, the Americas, or Oceania), or Eastern (Asian or African countries). 
Refraction
The determination of refractive error and visual acuity are described in detail elsewhere. 15,18 Briefly, best corrected visual acuity was determined in each candidate by a qualified optometrist using a standard Snellen chart. Those who read the 20/20 line with not more than one mistake were assumed to have no refractive error. 19 In subjects using optical correction, those who missed no more than one letter on the 20/20 line were assumed to be properly refracted. Other candidates underwent subjective noncycloplegic refraction. In some cases, the refractive error was recorded using paper documentation of the refraction performed by another optometrist. Only right eye data were used in the analyses. 
The spherical power and the cylinder power and axis were classified by using an approach previously reported. 10 According to this method, the level of spherical ametropia was defined as the least minus meridian power in myopic subjects and as the least plus meridian power in hyperopic subjects—that is, by the power of the cylinder axis with the least deviation from emmetropia (LDE). Subjects were included in the analysis as having astigmatism if they had cylinder power of 0.25 D or more. The 0.25 D cylinder power cutoff was chosen to conform with the classification of Farbrother et al., 10 thus permitting direct comparisons with the original analysis using the LDE refraction classification scheme. As in their report, 10 subjects with mixed astigmatism were excluded from analysis. Using the axis of the correcting spectacle lens, negative cylinder axes 180 ± 15 were considered WTR, and negative cylinders axes 90 ± 15 were considered ATR. The intervening correcting axes are classified as oblique (OBL). 
Body Mass Index and Height
The body mass index (BMI) was calculated from the body weight and height using the formula BMI = (weight in kilograms)/(height in meters)2. The BMI was categorized separately for the males and females by dividing the distribution into tertiles. For males, the BMI categories 1, 2, and 3 were <20.05, 20.06 to 22.78, and >22.79 kg/m2, respectively; for females, <19.91, 19.92 to 22.58, and >22.59 kg/m2, respectively. Height was classified into quartiles separately for the males and females. 
Photoperiod Category
The method of calculating the photoperiod length in the 30 days after birth for each subject is described elsewhere. 15 The lengths of the light phases for the birth seasons were divided into 4 categories: 10.1 to 10.8, 10.81 to 12.2, 12.21 to 13.57, and 13.58 to 14.23 hours (means: 10.3, 11.5, 12.9, and 14 hours) for categories 1, 2, 3, and 4, respectively. 
Intelligence Score
The intelligence score used by the Israeli Defense Forces 20 is composed of subsets of arithmetic, similarities, Raven's Progressive Matrices, and a modified Otis-type verbal intelligence test. It is a validated measure of general intelligence equivalent to a normally distributed IQ. The intelligence scores of the conscript group were divided into three categories, low, average and high, with an approximately equal number of individuals in each category. 
Statistics
Cylinder power was categorized into four groups (0.25–1.00, 1.25–2.00, 2.25–3.00, and ≥3.25 D) and least deviation from emmetropia was categorized into five groups (≤ −4.25, −2.25 to −4.00, 0 to −2.00, +0.25 to +2.00, ≥ +2.25 D). A value of P < 0.05 was considered statistically significant. Univariate analyses were performed with the PEPI program. 21 The association of least deviation from emmetropia, cylinder size category, BMI category, and photoperiod category with WTR astigmatism was evaluated using the trend test. The association of origin and sex with WTR astigmatism was determined with the χ2 test. Multivariate analysis was performed in a logistic regression model (SPSS, ver. 12; SPSS Inc., Chicago, IL). 
For the study database, 3856 pairs of siblings were identified as having a common father through the father's index number (the mother's index number not being available). The axis of the younger brother served as a variable in the data set of the older brother to estimate the familial effect of the axis of the younger brother on the axis of the older brother. 
The eye examination is one of the compulsory requirements during the conscripts' medical examination, and therefore, informed consent was not needed. The study was approved by the Institutional Review Board (IRB) of the Israeli Defense Force Medical Corps. The University of Pennsylvania IRB determined that Penn participation (RAS) in this study was exempt from IRB review. The data were analyzed anonymously from the computerized database, and the subjects' privacy was protected according to the guidelines of the Declaration of Helsinki. 
Results
The inclusion criteria for the astigmatism analysis were met by 67,899 subjects (36,265 males and 31,634 females), or 20.6% of the conscript population. The mean age of the subjects was 17.3 years (SD 0.5; range, 16.1–22.0). The subjects' origin, sex, BMI, photoperiod category, cylinder size, and least deviation from emmetropia are recorded in Table 1 in relation to the cylinder axis category. Due to missing data, Table 1 has minor discrepancies in aggregate subject numbers. 
Table 1.
 
Associations with Astigmatism Axis
Table 1.
 
Associations with Astigmatism Axis
Parameter/Category ATR* WTR* OBL* Total†
Origin
    Israel 2,177 (45.5) 1,733 (36.2) 872 (18.2) 4,782 (7.1)
    Western 14,304 (46.2) 11,258 (36.3) 5,424 (17.5) 30,986 (45.7)
    Eastern 13,037 (40.7) 12,729 (39.7) 6,264 (19.6) 32,030 (47.2)
Sex
    Male 15,905 (43.9) 13,696 (37.8) 6,664 (18.4) 36,265 (53.4)
    Female 13,663 (43.2) 12,055 (38.1) 5,916 (18.7) 31,634 (46.6)
BMI category
    1 (smallest) 10,322 (45.54) 8,048 (35.51) 4,296 (18.95) 22,666 (33.38)
    2 9,875 (43.81) 8,426 (37.38) 4,242 (18.82) 22,543 (33.2)
    3 (largest) 9,371 (41.3) 9,277 (40.89) 4,042 (17.81) 22,690 (33.42)
Photoperiod category
    1 (shortest) 7,763 (45.7) 6,075 (35.8) 3,139 (18.5) 16,977 (25)
    2 7,334 (44.1) 6,210 (37.3) 3,085 (18.6) 16,629 (24.5)
    3 7,248 (42.5) 6,683 (39.2) 3,113 (18.3) 17,044 (25.1)
    4 (longest) 7,223 (41.9) 6,783 (39.3) 3,243 (18.8) 17,249 (25.4)
Cylinder size category
    −0.25 to −1.0 25,248 (45.6) 19,111 (34.5) 11,027 (19.9) 55,386 (81.6)
    −1.25 to −2.0 3,629 (39.1) 4,481 (48.3) 1,177 (12.7) 9,287 (13.7)
    −2.25 to −3.0 495 (23.8) 1,332 (64.1) 250 (12) 2,077 (3.1)
    ≤−3.25 196 (17.1) 827 (72) 126 (11) 1,149 (1.7)
Least deviation from emmetropia
    ≤−4.25 2,895 (28.2) 5,403 (52.7) 1,953 (19.1) 10,251 (15.1)
    −2.25 to −4.0 6,482 (41.8) 6,129 (39.5) 2,896 (18.7) 15,507 (22.8)
    0 to −2.0 18,957 (49.1) 12,690 (32.8) 7,000 (18.1) 38,647 (56.9)
    +0.25 to +2.0 874 (36.1) 1,035 (42.7) 515 (21.2) 2,424 (3.6)
    ≥ +2.25 360 (33.6) 494 (46.2) 216 (20.2) 1,070 (1.6)
Intelligence score
    Low 8,278 (40.31) 8,206 (39.96) 4,054 (19.74) 20,538 (30.4)
    Medium 11,787 (44.33) 9,935 (37.36) 4,870 (18.31) 26,592 (39.3)
    High 9,405 (45.89) 7,495 (36.57) 3,593 (17.53) 20,493 (30.3)
Brother axis category
    WTR 409 (30.78) 704 (52.97) 216 (16.25) 1,329 (34.5)
    ATR 889 (51.72) 558 (32.46) 272 (15.82) 1,719 (44.6)
    OBL 365 (45.17) 320 (39.6) 123 (15.22) 808 (21.0)
Height category
    1 (smallest) 8,278 (44.7) 6,744 (36.4) 3,489 (18.8) 18,511 (27.3)
    2 7,965 (44.1) 6,758 (37.5) 3,318 (18.4) 18,041 (26.6)
    3 6,410 (42.7) 5,811 (38.7) 2,785 (18.6) 15,006 (22.1)
    4 (highest) 6,915 (42.3) 6,438 (39.4) 2,988 (18.3) 16,341 (24.1)
Total 29,568 (43.55) 25,751 (37.93) 12,580 (18.53) 67,899 (100)
Among recruits with astigmatism, those of Eastern origin had significantly more WTR cylinder axis than did subjects of Israeli origin (χ2 = 21.56, P < 0.001) or Western origin (χ2 = 77.6, P < 0.001). There was no significant difference in axis between subjects of Israeli and Western origin. The subject's sex was not associated with cylinder axis (χ2 = 2.025, P = 0.155). There was a higher prevalence of WTR astigmatism among those with higher ametropia than among those with lower ametropia (Fig. 1); the result of test for trend for the association between the prevalence of WTR, compared with that for the non-WTR axis, was statistically significant (χ2 = 1352.36, P < 0.001). The opposite association was present for ATR astigmatism (Fig. 1) and was statistically significant (trend test χ2 = 1860, P < 0.001). The association between LDE and OBL axis prevalence (Fig. 1) was in the same direction as that of the WTR axis (i.e., more prevalent in higher degrees of ametropia) but of considerably lower magnitude (trend test χ2 = 5.75, P = 0.016). 
Figure 1.
 
Astigmatism axis versus LDE. The proportion of subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the LDE.
Figure 1.
 
Astigmatism axis versus LDE. The proportion of subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the LDE.
For cylinder power and axis (Fig. 2), higher cylinder size was associated with greater WTR prevalence (trend test χ2 = 1856.9, P < 0.001). In contrast, ATR was much more common with smaller cylinder sizes (trend test χ2 = 790.1, P < 0.001). As with ATR axis but with lower magnitude, the prevalence of OBL astigmatism was greater with lower cylinder power (trend test χ2 = 321.9, P < 0.001). 
Figure 2.
 
Cylinder axis according to cylinder size. The proportion subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the cylinder size category.
Figure 2.
 
Cylinder axis according to cylinder size. The proportion subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the cylinder size category.
The combined effect of the cylinder power and the sphere power on the cylinder axis (WTR/ATR prevalence ratio) is shown in Figure 3. Some groups (higher LDE and higher cylinder power) contained more than four times the number of subjects with WTR astigmatism than with ATR astigmatism. In other combinations (e.g., near emmetropic LDE and small cylinder power), there were slightly more subjects with ATR astigmatism than with WTR astigmatism. 
Figure 3.
 
The combined effect of cylinder size and LDE on the prevalence ratio of WTR and ATR axes in astigmatic subjects. The WTR/ATR prevalence ratios, showing the combined effects of cylinder power and LDE. The bars with the filled black tops have WTR/ATR ratios between 0 and 1. All other bars have ratios >1.0.
Figure 3.
 
The combined effect of cylinder size and LDE on the prevalence ratio of WTR and ATR axes in astigmatic subjects. The WTR/ATR prevalence ratios, showing the combined effects of cylinder power and LDE. The bars with the filled black tops have WTR/ATR ratios between 0 and 1. All other bars have ratios >1.0.
For each sex, ATR axis was more prevalent than WTR axis among subjects with BMI of up to the 70th percentile (Fig. 4, Table 1). For each sex, ATR axis became less prevalent, and WTR axis became more prevalent with increasing BMI (trend test χ2 = 139.36, P < 0.001). The prevalence of OBL astigmatism was slightly less prevalent in increasing BMI (trend test χ2 = 9.8, P = 0.002). 
Figure 4.
 
Relation to BMI to astigmatism axis. The relation of BMI to WTR, ATR, or OBL astigmatism axes for male or female (Fem) subjects.
Figure 4.
 
Relation to BMI to astigmatism axis. The relation of BMI to WTR, ATR, or OBL astigmatism axes for male or female (Fem) subjects.
WTR axis was slightly more common in subjects born in months with longer photoperiods than in subjects born in months with shorter photoperiods (Table 1, trend test χ2 = 56.4, P < 0.001). In contrast, ATR axis was more common in subjects born in months with shorter photoperiods (Table 1, trend test χ2 = 59.84, P < 0.001). The prevalence of OBL astigmatism was not affected by the environmental photoperiod just after birth (χ2 = 0.24, P = 0.62). 
Regarding intelligence testing, the mean LDE of subjects in the low, medium, and high intelligence score categories were −1.7514, −1.9970, and −2.2625 D, respectively (P < 0.001 for between-group differences, ANOVA). The mean cylinder sizes in subjects in the low, medium, and high intelligence score categories were −0.8713, −0.8245, and −0.8078, respectively (P < 0.001 for between-group differences, ANOVA). For cylinder axis (Table 1, Fig. 5), higher intelligence scores were associated with a higher prevalence of ATR axes (trend test: χ2 = 130.32, P < 0.001) and a lower prevalence of WTR axes (trend test: χ2 = 49.86, P < 0.001). Higher intelligence also was associated with a decreased prevalence of OBL axes (trend test χ2 = 33.11, P < 0.001). 
Figure 5.
 
Relation of intelligence scores and cylinder axis. The relation of intelligence scores to WTR, ATR, or OBL astigmatism axes
Figure 5.
 
Relation of intelligence scores and cylinder axis. The relation of intelligence scores to WTR, ATR, or OBL astigmatism axes
Using the methods described, we identified 3856 subjects with at least one sibling with astigmatism. Analysis of these families revealed that the cylinder axes of siblings were associated. That is, when the first sibling had WTR astigmatism, the prevalences of WTR and ATR astigmatism axis in the second brother were 53.0% and 30.8%, respectively. Similarly, when the first sibling had ATR axis, this pattern was reversed and the prevalences of the axis types of the second brother were 32.5% and 51.7% for WTR and ATR axis, respectively. This association was statistically significant (χ2 = 154.9, P < 0.001). OBL axis prevalence was not affected by sibling axis (χ2 = 0.4, P = 0.818). 
Multivariate logistic regression revealed that being female and of non-Western origin, higher LDE categories, higher cylinder power, higher BMI, and longer post-natal photoperiod were all significantly and independently correlated with WTR axis, whereas higher intelligence scores were associated with a reduced prevalence of WTR axis (Table 2). 
Table 2.
 
Multivariate Logistic Regression of Parameters Associated with WTR Axis
Table 2.
 
Multivariate Logistic Regression of Parameters Associated with WTR Axis
Variable OR (95% CI) P *
Origin
    Western 1.00 (ref) 0.000†
    Israel 1.00 (0.94–1.07) 0.901
    Eastern 1.17 (1.13–1.21) 0.000
Sex
    Male 1.00 (ref) 0.011†
    Female 1.04 (1.01–1.08) 0.011
BMI
    1 1.00 (ref) 0.000†
    2 1.10 (1.06–1.14) 0.000
    3 1.25 (1.20–1.30) 0.000
Photoperiod category
    1 1.00 (ref) 0.000†
    2 1.07 (1.02–1.12) 0.003
    3 1.16 (1.11–1.22) 0.000
    4 1.17 (1.11–1.22) 0.000
Cylinder size
    −0.25 to −1.0 1.00 (ref) 0.000†
    −1.25 to −2.0 1.65 (1.58–1.72) 0.000
    −2.25 to −3.0 3.16 (2.88–3.47) 0.000
    ≥−3.25 4.60 (4.03–5.25) 0.000
Least deviation from emmetropia
    0 to −2.0 1.00 (ref) 0.000†
    ≤ −4.25 2.17 (2.07–2.27) 0.000
    −2.25 to −4.0 1.33 (1.28–1.39) 0.000
    +0.25 to +2.0 1.45 (1.33–1.58) 0.000
    ≥ +2.25 1.62 (1.43–1.84) 0.000
Intelligence score
    Low 1.00 (ref) 0.000†
    Med 0.90 (0.86–0.93) 0.000
    High 0.87 (0.83–0.91) 0.000
Height
    1 1.00 (ref) 0.000†
    2 1.06 (1.01–1.11) 0.01
    3 1.12 (1.07–1.18) 0.000
    4 1.17 (1.12–1.22) 0.000
When available sibling refractive data for the 3852 available subjects were included as an independent parameter in the regression model, the subjects' cylinder axis was found to be associated with their siblings' cylinder axis (odds ratio [OR] = 1.58; 95% confidence interval [CI] = 1.31–1.90). A WTR axis was found to be associated with cylinder size, least deviation from myopia, and BMI (Table 3). In this model, origin and photoperiod had marginal statistical significance based on the OR, and the intelligence score was not found to have an effect on cylinder axis orientation. 
Table 3.
 
Influence of Sibling Astigmatism
Table 3.
 
Influence of Sibling Astigmatism
Variable OR (95% CI)* P
Sibling axis
    OBL 1.00 (ref) 0.000
    WTR 1.58 (1.31–1.90) 0.000
    ATR 0.88 (0.61–0.735) 0.000
Origin
    Western 1.00 (ref) 0.051
    Israel 1.16 (0.88–1.55) 0.298
    Eastern 1.2 (1.03–1.39) 0.16
Sex
    Male 1 (ref) 0.560
    Female 1.04 (0.91–1.2) 0.560
BMI
    1 1.00 (ref) 0.000
    2 1.12 (0.95–1.32) 0.162
    3 1.41 (1.20–1.67) 0.000
Photoperiod category
    1 1.00 (ref) 0.052
    2 1.03 (0.86–1.26) 0.702
    3 1.26 (1.04–1.52) 0.017
    4 1.20 (0.99–1.45) 0.063
Cylinder Size
    −0.25 to −1.0 1.00 (ref) 0.000
    −1.25 to −2.0 1.47 (1.26–1.72) 0.000
    −2.25 to −3.0 2.87 (2.14–3.84) 0.000
    ≥−3.25 3.13 (2.07–4.72) 0.000
Least deviation from emmetropia
    0 to −2.0 1.00 (ref) 0.000
    ≤ −4.25 2.47 (2.08–2.92) 0.000
    −2.25 to −4.0 1.32 (1.12–1.55) 0.001
    +0.25 to +2.0 1.44 (0.89–2.33) 0.133
    ≥ +2.25 1.24 (0.63–2.44) 0.528
Intelligence score
    Low 1.00 (ref) 0.537
    Medium 0.95 (0.81–1.12) 0.558
    High 0.9 (0.75–1.08) 0.265
Discussion
By directing analysis toward the power and axis of astigmatism, this study reveals several associations between cylindrical refractive errors and parameters related to the subjects' overall refractive status, to their individual and familial characteristics, and to available potential early life environmental exposures. It has long been appreciated that incorporating astigmatism complicates the classification of the refractive status of individual subjects. 11,22 In the common spherical equivalent notation (spherical power + half of the cylinder power) or a more recently proposed transformation of refraction values through Fourier analysis, 23 as examples, the spherical component of refraction is influenced arithmetically by the power of the cylinder. Since both the spherical power and cylindrical power occur in the same eye, they are not strictly independent either biologically or statistically. Whether the developmental mechanisms causing spherical and cylindrical ametropia are actually independent, however, is not known. In an effort to separate at least mathematically the spherical and cylindrical powers, Guggenheim and Farbrother 22 have proposed the LDE (least deviation from emmetropia) classification scheme incorporated here. 
Applying this LDE classification scheme to a large population of Israeli military conscripts revealed complex relationships between the spherical power and the cylindrical axis and power (Figs. 1 23). With LDE refractions deviating from emmetropia in either the myopic or hyperopic direction, WTR astigmatic axes became more prevalent with larger ametropia. For ATR axis, the opposite relationship held, with the largest proportion of ATR astigmatism occurring near emmetropia and with a decreasing prevalence as LDE increased in magnitude. In addition, cylinder axis was affected by cylinder power: the prevalence of WTR astigmatism increases with increasing cylinder power; that of ATR astigmatism decreases with increasing cylinder power. These complex relations between the prevalence of WTR and ATR astigmatism with LDE and cylinder powers conform to a prior report in which the same approach was used to classify refraction. 10 In addition, our large sample size permitted assessment of OBL astigmatism. Although the magnitude of the effects were comparatively small, the prevalence of OBL astigmatism increased with increasing ametropia in either direction similar to WTR astigmatism (Fig. 1); and the prevalence of OBL astigmatism decreased with increasing cylinder size, similar to ATR astigmatism (Fig. 2). 
Perhaps, the LDE notation used in our study and in a prior report 10 facilitated revealing these relationships between the cylinder direction and both spherical and cylindrical powers. These results suggest a hypothesis that, at least for the teenagers and young adults whom we studied, risk factors for WTR or OBL astigmatism and spherical ametropias may be similar, but the risk factors for ATR astigmatism may differ from those for underlying spherical ametropia (Fig. 1). Conceivably, risk factors for ATR astigmatism may even be protective against ametropia. The reducing prevalence of ATR axis and OBL axis with increasing cylinder power (Fig. 2) also raises the possibility of different risk factors for the two parameters of axis orientation and astigmatism power. However, the present study was a cross-sectional survey that assessed only astigmatic subjects and not a prospective study, and validating such causative hypotheses will require more definitive methods in the future. 
Both mechanical and nonmechanical causes have been invoked as a basis for astigmatism. Most commonly discussed are mechanical hypotheses, such as the exertion of tension from extraocular muscles or eyelid weight on the cornea. 7 Eyelid anatomy, orbital anatomy, and related external pressures on the globe have been associated with astigmatism axis and corneal shape. 24,25 Transient effects of eye position on corneal astigmatism are generally assumed to result from an altered relationship of the eyelid and cornea, 26 but the action of the extraocular muscles cannot strictly be excluded in such evaluations. Eyelid surgery can have modest effects on corneal astigmatism, 27 but the effect may be transient in many patients. 28 On the other hand, the lack of correlation between corneal toricity and direct measurements of eyelid tension 29 and the marked differences in cylinder orientation between Chinese and Caucasian infants 30 suggest that other nonmechanical factors may be at least partly responsible for astigmatism. The balancing of corneal and internal sources of astigmatism to reduce the toricity in individual eyes 31 also suggests a role for nonmechanical biological processes in generating astigmatism, as now seemingly underlies refractive errors in general. 12  
Although they were not as pronounced as in other studies reporting the ethnic differences in the prevalence of astigmatism, 68,31 we did detect modest differences in the proportion of WTR, ATR, or OBL axes among astigmatic conscripts whose families originated from different geographic regions. Israeli and Eastern ethnic origin were associated with more WTR axis compared with Western origin. Ethnic differences in astigmatism axis conform with a prior study from Australia 31 that found higher proportions of WTR and less ATR astigmatism axis in children of non–European Caucasian ethnicity compared to children of Asian ethnicity. Whether the effect of Israeli conscript origin on astigmatism prevalence are explainable as differences in genetic admixing in prior generations, by differences in living environments in Israel 6,32 or perhaps by ethnic differences in orbital and lid structure cannot be assessed from the current data. 
Indices of body stature have repeatedly been studied in association with refractive errors, most commonly as spherical ametropias; but results vary between studies, and the mechanisms relating body stature and refraction are poorly understood. 3335 In the present Israeli conscript data, WTR astigmatism increased with increasing BMI (Fig. 4), but the prevalence of both ATR and OBL astigmatism decreased with increasing BMI. Perhaps, the higher prevalence of WTR in obese compared with nonobese young adults may be explainable by a rise in eyelid tension on the globe with increasing body weight and a resultant steepening of the corneal vertical meridian and WTR astigmatism. 
Higher intelligence, as measured by standard tests, has long been associated with increased myopia prevalence. 36,37 Similarly, in the current data, higher intelligence scores were associated with greater myopia. In addition, we found that higher intelligence scores were associated with lower magnitude of cylinder power, higher prevalence of ATR axis orientation, and lower prevalence of both WTR and OBL axis orientations. Of note, the associations of intelligence with astigmatism parameters were dissociated from the associations of intelligence with the spherical component of refraction based on the following considerations. Intelligence scores increased with increasing myopia, with decreasing cylinder power, and with higher prevalence of ATR axis orientations; but increasing myopic LDE was associated with less ATR axis (Fig. 1), precisely the opposite direction anticipated if the associations with intelligence scores were consistent across all refractive parameters. 
Although the effect was comparatively small, photoperiod length at the time of birth also showed complex associations with cylinder axis. Among the astigmatic subjects, the prevalence of WTR axes increased with birthdates in the months with longer photoperiods (Table 1). In this population, higher degrees of myopia had been associated with birthdates in months with longer photoperiod. 15 Because WTR axes also increased with increasing hyperopic LDE (Fig. 1), the photoperiod relationships suggest differences in the risk factors for the astigmatic and spherical components of refraction. The association between astigmatism and season of birth or perinatal photoperiod, identified in this study, further emphasizes the potential influence of perinatal or neonatal environmental parameters on refractive development (Fotedar R, et al. IOVS 2008;49:ARVO E-Abstract 3142). 13,14 As recently discussed, 15,17 it is not known whether the birth date and photoperiod associations with refraction are causal or instead reveal the influences of different environmental parameters. In fact, available data do not distinguish whether the primary influence acts directly on the infant after birth or indirectly through the mother during pregnancy or breastfeeding. For instance, photoperiod may associate with seasonal differences in ambient temperature or diet that have not been investigated in relation to subsequent refractive development. Despite much research, the role of environmental parameters in refractive development remains poorly understood. That perinatal or neonatal environmental parameters might exert long-term influences on refraction is an evolving, novel, and yet controversial notion. Clearly, more research is needed to further advance the mechanistic understanding in this field. 
In our study, being female was associated with slightly more WTR axis compared with being male, an association that was statistically significant in multivariate but not in univariate analysis. Although the relations of astigmatism and sex have varied in prior studies, our results are consistent with those in a recent report 31 of a higher percentage of WTR and lower percentage of OBL astigmatism in females. In another recent report in which both astigmatism and features of eyelid anatomy were examined, astigmatism axis correlated with the orientation of the palpebral fissure slant; as the females had more of an upward palpebral fissure slant in the Caucasian and African-American subjects studied, the sex difference in cylinder axis orientation may relate to such sex-related differences in the orientation of the lid fissures. 38 Nonmechanical explanations for the sex effect are also possible, although, as was observed in a small study, a correlation of lower blood estrogen levels and increased horizontal corneal curvature in postmenopausal women. 39  
Several methodological considerations are pertinent to the associations found in the present study. First is the use of the recent LDE approach for refraction classifications. Many notations for refractive error are available; but for most, the astigmatism power affects and thus confounds the spherical classification. Although not without its own peculiarities, the LDE notation at least minimizes this sort of potential classification error. Second, we included data from right eyes only. Although a common approach in many studies of refraction to avoid statistical confounding by nonindependence of the two eyes, including only right eyes precludes addressing either direct or mirror symmetry of astigmatism between the eyes of individual subjects. 40  
Total astigmatism as measured in this study results from the combination of corneal and internal astigmatism, the latter chiefly deriving from the ocular lens. 7 In population averages, internal astigmatism tends to be small in power and ATR in orientation, but with some individual variability. 41,42 Because keratometry readings are not included in the conscription eye examination, we cannot reliably distinguish the corneal versus internal origins of overall ocular astigmatism in our subjects. How the parameters that we studied relate to corneal and internal astigmatism and whether the association patterns are similar or distinct will certainly be informative questions for future research. 
In the present analysis, we were not able to exclude data from subjects with ocular or systemic diseases that have might have secondarily affected astigmatism. However, in a similar (and partially parallel) sample of refraction data from the Israeli Defense Forces, the prevalence of keratoconus among the astigmatic population was estimated to be <0.4:1000 (Mandel Y, unpublished data, 2009). Moreover, subjects with severe systemic diseases are usually excluded from military service and would not routinely be refracted or have been included in the current data set. Thus, we believe that the prevalence of ocular or systemic conditions potentially influencing astigmatism is small and unlikely to be inducing a significant bias. 
The present analysis necessarily depended on data available only from the preconscription examination; but the large sample size, comparatively homogeneous population, and narrow age range are likely to minimize potential confounding in the findings. Two striking conclusions emerged from the summary provided in Table 4. First, the associations with ATR, WTR, and OBL astigmatism axes were neither parallel as a whole nor parallel between any two sets of axis orientations. Second, the directions of the associations with astigmatism axis and astigmatism power did not parallel previously reported associations for spherical ametropias. For instance, both WTR astigmatism and myopia prevalence increased with increasing birth month photoperiod in this population 15 ; but WTR astigmatism prevalence decreased with increasing intelligence, just the opposite association long found for myopia and intelligence. 36,37 Although refractive development can continue beyond the beginning of the third decade, the refractions of military aged subjects should represent relatively mature ocular development. Many of the epidemiologic parameters studied here have long been incorporated in refractive research. Presumably, such readily identifiable clinical parameters are surrogate markers, however imperfect, for the molecular and cellular mechanisms that govern the growth and form of the eye. To the extent that associations with these clinical parameters may reveal the underlying biological mechanism of refractive errors, the complexity of the present findings suggests both that dissimilar mechanisms are responsible for the different forms of astigmatism and that mechanisms governing development of astigmatism likely diverge from those governing the spherical component of refraction. 
Table 4.
 
Effects of Various Parameters on Cylinder Power and Axis
Table 4.
 
Effects of Various Parameters on Cylinder Power and Axis
Parameter Cylinder Power Cylinder Axis Orientation
ATR WTR OBL*
Increasing myopic LDE
Increasing hyperopic LDE ↑↓†
Increasing cylinder power
Increasing BMI
Increasing birth month photoperiod
Increasing intelligence score
Sibling WTR axis
Footnotes
 Supported by The Paul and Evanina Bell Mackall Foundation Trust (RAS) and Research to Prevent Blindness (RAS).
Footnotes
 Disclosure: Y. Mandel, None; R.A. Stone, None; D. Zadok, None
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Figure 1.
 
Astigmatism axis versus LDE. The proportion of subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the LDE.
Figure 1.
 
Astigmatism axis versus LDE. The proportion of subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the LDE.
Figure 2.
 
Cylinder axis according to cylinder size. The proportion subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the cylinder size category.
Figure 2.
 
Cylinder axis according to cylinder size. The proportion subjects with WTR, ATR, or OBL astigmatism among the total population with astigmatism is shown as a function of the cylinder size category.
Figure 3.
 
The combined effect of cylinder size and LDE on the prevalence ratio of WTR and ATR axes in astigmatic subjects. The WTR/ATR prevalence ratios, showing the combined effects of cylinder power and LDE. The bars with the filled black tops have WTR/ATR ratios between 0 and 1. All other bars have ratios >1.0.
Figure 3.
 
The combined effect of cylinder size and LDE on the prevalence ratio of WTR and ATR axes in astigmatic subjects. The WTR/ATR prevalence ratios, showing the combined effects of cylinder power and LDE. The bars with the filled black tops have WTR/ATR ratios between 0 and 1. All other bars have ratios >1.0.
Figure 4.
 
Relation to BMI to astigmatism axis. The relation of BMI to WTR, ATR, or OBL astigmatism axes for male or female (Fem) subjects.
Figure 4.
 
Relation to BMI to astigmatism axis. The relation of BMI to WTR, ATR, or OBL astigmatism axes for male or female (Fem) subjects.
Figure 5.
 
Relation of intelligence scores and cylinder axis. The relation of intelligence scores to WTR, ATR, or OBL astigmatism axes
Figure 5.
 
Relation of intelligence scores and cylinder axis. The relation of intelligence scores to WTR, ATR, or OBL astigmatism axes
Table 1.
 
Associations with Astigmatism Axis
Table 1.
 
Associations with Astigmatism Axis
Parameter/Category ATR* WTR* OBL* Total†
Origin
    Israel 2,177 (45.5) 1,733 (36.2) 872 (18.2) 4,782 (7.1)
    Western 14,304 (46.2) 11,258 (36.3) 5,424 (17.5) 30,986 (45.7)
    Eastern 13,037 (40.7) 12,729 (39.7) 6,264 (19.6) 32,030 (47.2)
Sex
    Male 15,905 (43.9) 13,696 (37.8) 6,664 (18.4) 36,265 (53.4)
    Female 13,663 (43.2) 12,055 (38.1) 5,916 (18.7) 31,634 (46.6)
BMI category
    1 (smallest) 10,322 (45.54) 8,048 (35.51) 4,296 (18.95) 22,666 (33.38)
    2 9,875 (43.81) 8,426 (37.38) 4,242 (18.82) 22,543 (33.2)
    3 (largest) 9,371 (41.3) 9,277 (40.89) 4,042 (17.81) 22,690 (33.42)
Photoperiod category
    1 (shortest) 7,763 (45.7) 6,075 (35.8) 3,139 (18.5) 16,977 (25)
    2 7,334 (44.1) 6,210 (37.3) 3,085 (18.6) 16,629 (24.5)
    3 7,248 (42.5) 6,683 (39.2) 3,113 (18.3) 17,044 (25.1)
    4 (longest) 7,223 (41.9) 6,783 (39.3) 3,243 (18.8) 17,249 (25.4)
Cylinder size category
    −0.25 to −1.0 25,248 (45.6) 19,111 (34.5) 11,027 (19.9) 55,386 (81.6)
    −1.25 to −2.0 3,629 (39.1) 4,481 (48.3) 1,177 (12.7) 9,287 (13.7)
    −2.25 to −3.0 495 (23.8) 1,332 (64.1) 250 (12) 2,077 (3.1)
    ≤−3.25 196 (17.1) 827 (72) 126 (11) 1,149 (1.7)
Least deviation from emmetropia
    ≤−4.25 2,895 (28.2) 5,403 (52.7) 1,953 (19.1) 10,251 (15.1)
    −2.25 to −4.0 6,482 (41.8) 6,129 (39.5) 2,896 (18.7) 15,507 (22.8)
    0 to −2.0 18,957 (49.1) 12,690 (32.8) 7,000 (18.1) 38,647 (56.9)
    +0.25 to +2.0 874 (36.1) 1,035 (42.7) 515 (21.2) 2,424 (3.6)
    ≥ +2.25 360 (33.6) 494 (46.2) 216 (20.2) 1,070 (1.6)
Intelligence score
    Low 8,278 (40.31) 8,206 (39.96) 4,054 (19.74) 20,538 (30.4)
    Medium 11,787 (44.33) 9,935 (37.36) 4,870 (18.31) 26,592 (39.3)
    High 9,405 (45.89) 7,495 (36.57) 3,593 (17.53) 20,493 (30.3)
Brother axis category
    WTR 409 (30.78) 704 (52.97) 216 (16.25) 1,329 (34.5)
    ATR 889 (51.72) 558 (32.46) 272 (15.82) 1,719 (44.6)
    OBL 365 (45.17) 320 (39.6) 123 (15.22) 808 (21.0)
Height category
    1 (smallest) 8,278 (44.7) 6,744 (36.4) 3,489 (18.8) 18,511 (27.3)
    2 7,965 (44.1) 6,758 (37.5) 3,318 (18.4) 18,041 (26.6)
    3 6,410 (42.7) 5,811 (38.7) 2,785 (18.6) 15,006 (22.1)
    4 (highest) 6,915 (42.3) 6,438 (39.4) 2,988 (18.3) 16,341 (24.1)
Total 29,568 (43.55) 25,751 (37.93) 12,580 (18.53) 67,899 (100)
Table 2.
 
Multivariate Logistic Regression of Parameters Associated with WTR Axis
Table 2.
 
Multivariate Logistic Regression of Parameters Associated with WTR Axis
Variable OR (95% CI) P *
Origin
    Western 1.00 (ref) 0.000†
    Israel 1.00 (0.94–1.07) 0.901
    Eastern 1.17 (1.13–1.21) 0.000
Sex
    Male 1.00 (ref) 0.011†
    Female 1.04 (1.01–1.08) 0.011
BMI
    1 1.00 (ref) 0.000†
    2 1.10 (1.06–1.14) 0.000
    3 1.25 (1.20–1.30) 0.000
Photoperiod category
    1 1.00 (ref) 0.000†
    2 1.07 (1.02–1.12) 0.003
    3 1.16 (1.11–1.22) 0.000
    4 1.17 (1.11–1.22) 0.000
Cylinder size
    −0.25 to −1.0 1.00 (ref) 0.000†
    −1.25 to −2.0 1.65 (1.58–1.72) 0.000
    −2.25 to −3.0 3.16 (2.88–3.47) 0.000
    ≥−3.25 4.60 (4.03–5.25) 0.000
Least deviation from emmetropia
    0 to −2.0 1.00 (ref) 0.000†
    ≤ −4.25 2.17 (2.07–2.27) 0.000
    −2.25 to −4.0 1.33 (1.28–1.39) 0.000
    +0.25 to +2.0 1.45 (1.33–1.58) 0.000
    ≥ +2.25 1.62 (1.43–1.84) 0.000
Intelligence score
    Low 1.00 (ref) 0.000†
    Med 0.90 (0.86–0.93) 0.000
    High 0.87 (0.83–0.91) 0.000
Height
    1 1.00 (ref) 0.000†
    2 1.06 (1.01–1.11) 0.01
    3 1.12 (1.07–1.18) 0.000
    4 1.17 (1.12–1.22) 0.000
Table 3.
 
Influence of Sibling Astigmatism
Table 3.
 
Influence of Sibling Astigmatism
Variable OR (95% CI)* P
Sibling axis
    OBL 1.00 (ref) 0.000
    WTR 1.58 (1.31–1.90) 0.000
    ATR 0.88 (0.61–0.735) 0.000
Origin
    Western 1.00 (ref) 0.051
    Israel 1.16 (0.88–1.55) 0.298
    Eastern 1.2 (1.03–1.39) 0.16
Sex
    Male 1 (ref) 0.560
    Female 1.04 (0.91–1.2) 0.560
BMI
    1 1.00 (ref) 0.000
    2 1.12 (0.95–1.32) 0.162
    3 1.41 (1.20–1.67) 0.000
Photoperiod category
    1 1.00 (ref) 0.052
    2 1.03 (0.86–1.26) 0.702
    3 1.26 (1.04–1.52) 0.017
    4 1.20 (0.99–1.45) 0.063
Cylinder Size
    −0.25 to −1.0 1.00 (ref) 0.000
    −1.25 to −2.0 1.47 (1.26–1.72) 0.000
    −2.25 to −3.0 2.87 (2.14–3.84) 0.000
    ≥−3.25 3.13 (2.07–4.72) 0.000
Least deviation from emmetropia
    0 to −2.0 1.00 (ref) 0.000
    ≤ −4.25 2.47 (2.08–2.92) 0.000
    −2.25 to −4.0 1.32 (1.12–1.55) 0.001
    +0.25 to +2.0 1.44 (0.89–2.33) 0.133
    ≥ +2.25 1.24 (0.63–2.44) 0.528
Intelligence score
    Low 1.00 (ref) 0.537
    Medium 0.95 (0.81–1.12) 0.558
    High 0.9 (0.75–1.08) 0.265
Table 4.
 
Effects of Various Parameters on Cylinder Power and Axis
Table 4.
 
Effects of Various Parameters on Cylinder Power and Axis
Parameter Cylinder Power Cylinder Axis Orientation
ATR WTR OBL*
Increasing myopic LDE
Increasing hyperopic LDE ↑↓†
Increasing cylinder power
Increasing BMI
Increasing birth month photoperiod
Increasing intelligence score
Sibling WTR axis
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